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TZID:Asia/Jerusalem
BEGIN:STANDARD
DTSTART:20151025T020000
TZOFFSETFROM:+0300
TZOFFSETTO:+0200
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DTSTART:20160325T020000
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UID:calendar.44834.field_date.0@mathematics.huji.ac.il
DTSTAMP:20191122T161343Z
CREATED:20171116T060001Z
DESCRIPTION:Date: \n\n2:00pm to 3:00pm\n\n\n\n\nSee also: Dynamical & Pro
bability\, Events & Seminars\, SeminarsLocation: \n\nManchester building\,
Hebrew University of Jerusalem\, (Room 209)\n\n\nTitle: Self-affine measu
res with equal Hausdorff and Lyapunov dimensions\n\nAbstract:\nLet μ be th
e stationary measure on ℝd which corresponds to a self-affine iterated fun
ction system Φ and a probability vector p. Denote by A⊂Gl(d\,ℝ) the linear
parts of Φ. Assuming the members of A contract by more than 12\, it follo
ws from a result by Jordan\, Pollicott and Simon\, that if the translation
s of Φ are drawn according to the Lebesgue measure\, then dimHμ=min{D\,d}
almost surely. Here D is the Lyapunov dimension\, which is an explicit con
stant defined in terms of A and p.\n\nI will present a new result which pr
ovides general conditions for μ to be exact dimensional with dimμ=D\, when
ever Φ satisfies strong separation. These conditions involve a lower bound
on the dimension of the Furstenberg measure corresponding to A and p. The
proof uses random matrix theory\, and upper bounds on the dimension of ex
ceptional sets of sections and projections of measures.\n\nBy using this I
will present new explicit examples of self-affine measures whose dimensio
n can be computed. These examples rely on new results by Hochman and Solom
yak\, Bourgain\, and Benoist and Quint\, regarding the Furstenberg measure
.\n\n Export\n \n\n \nsubscribe iCal
DTSTART;TZID=Asia/Jerusalem:20151110T140000
DTEND;TZID=Asia/Jerusalem:20151110T150000
LAST-MODIFIED:20171228T140836Z
SUMMARY:Dynamics & probability: Ariel Rapaport (HUJI) ' Self-affine measure
s with equal Hausdorff and Lyapunov dimensions'
URL;TYPE=URI:https://mathematics.huji.ac.il/event/dynamics-probability-arie
l-rapaport-huji-self-affine-measures-equal-hausdorff-and-lyapunov
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